diffsol 0.1.9

A library for solving ordinary differential equations (ODEs) in Rust.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152

use crate::{
    ode_solver::problem::OdeSolverSolution, Matrix, OdeBuilder, OdeEquations, OdeSolverProblem,
    Vector,
};
use num_traits::Zero;

pub fn robertson_ode_with_sens<M: Matrix + 'static>(
    use_coloring: bool,
) -> (
    OdeSolverProblem<impl OdeEquations<M = M, V = M::V, T = M::T>>,
    OdeSolverSolution<M::V>,
) {
    let problem = OdeBuilder::new()
        .p([0.04, 1.0e4, 3.0e7])
        .rtol(1e-4)
        .atol([1.0e-8, 1.0e-6, 1.0e-6])
        .use_coloring(use_coloring)
        .build_ode_with_sens(
            //     dy1/dt = -.04*y1 + 1.e4*y2*y3
            //*    dy2/dt = .04*y1 - 1.e4*y2*y3 - 3.e7*(y2)^2
            //*    dy3/dt = 3.e7*(y2)^2
            |x: &M::V, p: &M::V, _t: M::T, y: &mut M::V| {
                y[0] = -p[0] * x[0] + p[1] * x[1] * x[2];
                y[1] = p[0] * x[0] - p[1] * x[1] * x[2] - p[2] * x[1] * x[1];
                y[2] = p[2] * x[1] * x[1];
            },
            |x: &M::V, p: &M::V, _t: M::T, v: &M::V, y: &mut M::V| {
                y[0] = -p[0] * v[0] + p[1] * v[1] * x[2] + p[1] * x[1] * v[2];
                y[1] = p[0] * v[0]
                    - p[1] * v[1] * x[2]
                    - p[1] * x[1] * v[2]
                    - M::T::from(2.0) * p[2] * x[1] * v[1];
                y[2] = M::T::from(2.0) * p[2] * x[1] * v[1];
            },
            |x: &M::V, _p: &M::V, _t: M::T, v: &M::V, y: &mut M::V| {
                y[0] = -v[0] * x[0] + v[1] * x[1] * x[2];
                y[1] = v[0] * x[0] - v[1] * x[1] * x[2] - v[2] * x[1] * x[1];
                y[2] = v[2] * x[1] * x[1];
            },
            |_p: &M::V, _t: M::T| M::V::from_vec(vec![1.0.into(), 0.0.into(), 0.0.into()]),
            |_p: &M::V, _t: M::T, _v: &M::V, y: &mut M::V| y.fill(M::T::zero()),
        )
        .unwrap();

    let mut soln = OdeSolverSolution::default();
    let data = vec![
        (vec![1.0, 0.0, 0.0], 0.0),
        (vec![9.851641e-01, 3.386242e-05, 1.480205e-02], 0.4),
        (vec![9.055097e-01, 2.240338e-05, 9.446793e-02], 4.0),
        (vec![7.158017e-01, 9.185037e-06, 2.841892e-01], 40.0),
        (vec![4.505360e-01, 3.223271e-06, 5.494608e-01], 400.0),
        (vec![1.832299e-01, 8.944378e-07, 8.167692e-01], 4000.0),
        (vec![3.898902e-02, 1.622006e-07, 9.610108e-01], 40000.0),
        (vec![4.936383e-03, 1.984224e-08, 9.950636e-01], 400000.0),
        (vec![5.168093e-04, 2.068293e-09, 9.994832e-01], 4000000.0),
        (vec![5.202440e-05, 2.081083e-10, 9.999480e-01], 4.0000e+07),
        (vec![5.201061e-06, 2.080435e-11, 9.999948e-01], 4.0000e+08),
        (vec![5.258603e-07, 2.103442e-12, 9.999995e-01], 4.0000e+09),
        (vec![6.934511e-08, 2.773804e-13, 9.999999e-01], 4.0000e+10),
    ];

    for (values, time) in data {
        soln.push(
            M::V::from_vec(values.into_iter().map(|v| v.into()).collect()),
            time.into(),
        );
    }
    (problem, soln)
}

/* -----------------------------------------------------------------
 * Programmer(s): Scott D. Cohen, Alan C. Hindmarsh and
 *                Radu Serban @ LLNL
 * -----------------------------------------------------------------
 * SUNDIALS Copyright Start
 * Copyright (c) 2002-2023, Lawrence Livermore National Security
 * and Southern Methodist University.
 * All rights reserved.
 *
 * See the top-level LICENSE and NOTICE files for details.
 *
 * SPDX-License-Identifier: BSD-3-Clause
 * SUNDIALS Copyright End
 * -----------------------------------------------------------------
 * Example problem:
 *
 * The following is a simple example problem, with the coding
 * needed for its solution by CVODE. The problem is from
 * chemical kinetics, and consists of the following three rate
 * equations:
 *    dy1/dt = -.04*y1 + 1.e4*y2*y3
 *    dy2/dt = .04*y1 - 1.e4*y2*y3 - 3.e7*(y2)^2
 *    dy3/dt = 3.e7*(y2)^2
 * on the interval from t = 0.0 to t = 4.e10, with initial
 * conditions: y1 = 1.0, y2 = y3 = 0. The problem is stiff.
 * While integrating the system, we also use the rootfinding
 * feature to find the points at which y1 = 1e-4 or at which
 * y3 = 0.01. This program solves the problem with the BDF method,
 * Newton iteration with the dense linear solver, and a
 * user-supplied Jacobian routine.
 * It uses a scalar relative tolerance and a vector absolute
 * tolerance. Output is printed in decades from t = .4 to t = 4.e10.
 * Run statistics (optional outputs) are printed at the end.
 * -----------------------------------------------------------------*/

// 3-species kinetics problem

// At t = 2.6391e-01      y =  9.899653e-01    3.470564e-05    1.000000e-02
// rootsfound[] =   0   1
// At t = 4.0000e-01      y =  9.851641e-01    3.386242e-05    1.480205e-02
// At t = 4.0000e+00      y =  9.055097e-01    2.240338e-05    9.446793e-02
// At t = 4.0000e+01      y =  7.158017e-01    9.185037e-06    2.841892e-01
// At t = 4.0000e+02      y =  4.505360e-01    3.223271e-06    5.494608e-01
// At t = 4.0000e+03      y =  1.832299e-01    8.944378e-07    8.167692e-01
// At t = 4.0000e+04      y =  3.898902e-02    1.622006e-07    9.610108e-01
// At t = 4.0000e+05      y =  4.936383e-03    1.984224e-08    9.950636e-01
// At t = 4.0000e+06      y =  5.168093e-04    2.068293e-09    9.994832e-01
// At t = 2.0790e+07      y =  1.000000e-04    4.000397e-10    9.999000e-01
// rootsfound[] =  -1   0
// At t = 4.0000e+07      y =  5.202440e-05    2.081083e-10    9.999480e-01
// At t = 4.0000e+08      y =  5.201061e-06    2.080435e-11    9.999948e-01
// At t = 4.0000e+09      y =  5.258603e-07    2.103442e-12    9.999995e-01
// At t = 4.0000e+10      y =  6.934511e-08    2.773804e-13    9.999999e-01
//
// Final Statistics:
// Current time                 = 41154661313.59952
// Steps                        = 542
// Error test fails             = 22
// NLS step fails               = 0
// Initial step size            = 8.236259832589498e-14
// Last step size               = 4747036977.219155
// Current step size            = 4747036977.219155
// Last method order            = 4
// Current method order         = 4
// Stab. lim. order reductions  = 0
// RHS fn evals                 = 754
// NLS iters                    = 751
// NLS fails                    = 3
// NLS iters per step           = 1.385608856088561
// LS setups                    = 107
// Jac fn evals                 = 11
// LS RHS fn evals              = 0
// Prec setup evals             = 0
// Prec solves                  = 0
// LS iters                     = 0
// LS fails                     = 0
// Jac-times setups             = 0
// Jac-times evals              = 0
// LS iters per NLS iter        = 0
// Jac evals per NLS iter       = 0.01464713715046605
// Prec evals per NLS iter      = 0
// Root fn evals                = 570